What is the best approach for multivariable and multivariate regression?
You create a model like this very easily with keras. Follow these steps.
Data Exploring
Before building a machine learning model, you must explore your data first. An approach is to use libraries to visualize the data as graphs. You can use the tool pandas-profiling
https://towardsdatascience.com/exploring-your-data-with-just-1-line-of-python-4b35ce21a82d
Points to look for when exploring the data
You should look for the following:

Distribution of labels and input features
Range of input features and labels
Missing label or input feature
Nan on value
Outliers

You should look out for them and use appropriate data cleaning or filtering method to clean them. For example, Nan or missing value may be substituted with 0 and outliers will be removed. Input features may also be normalized.
Building the model
Keras is a easy tool for building machinea learning model. For how to build a basic MLP ( Multi-Layer Perceptron), you can refer to the example code and the resource.
https://machinelearningmastery.com/tutorial-first-neural-network-python-keras/
Experimenting
After creating the basic model, you can start experimenting with stuff like:

Different model structure like adding layers and changing hidden layer size
Different Optimizer
Different hyperparameters like learning rate and batch size
Different input features

You will gain more experience as you go. There is a lot of ways to improve the performance of the model.
Bewares
Here are things to beware:

If your model doesn't work out, don't worry. Try another method or tune parameters until it work.
If the testing loss become very high while training loss is low, you can add dropout to prevent this from happening. This is called overfitting.

Hope I can help you and have fun!